Step 1

In a large, heavy-bottomed Dutch oven, preferably cast-iron or enamel cast-iron, heat the oil over medium-high heat until shimmering. When a pinch of flour sprinkled on the oil immediately blooms on the surface of the oil, scatter in the rest of the flour and quickly stir, thoroughly combining the oil and flour into a thick, smooth roux.

Step 2

Continue cooking the roux, stirring often, as it turns from pale yellow to a rich, deep brown, adjusting the heat as needed to keep the roux slowly darkening without bubbling or burning. This can take anywhere from 20 to 60 minutes, depending on your pot and your stove. The finished roux should be darker than peanut butter and about the color of coffee with a little cream.

Step 3

Add the onion, celery, and bell pepper to the roux and stir well to coat them. Let them cook, stirring often, until the vegetables are fragrant, softened, shiny, and evenly coated with the roux, 2 to 3 minutes. Add the garlic, thyme, salt, pepper, paprika, and cayenne, and stir well and cook for 2 minutes more.

Step 4

Add the stock, stir well, and bring it to a lively boil, stirring often to dissolve the roux into the stock. When everything is boiling nicely, add the chicken. When the stock returns to a rolling boil, adjust the heat to maintain a lively simmer and cook, stirring now and then, until the chicken is cooked through and very tender, 45 minutes to 1 hour.

Step 5

Meanwhile, chop the andouille into bite-size pieces, first halving each andouille link lengthwise and then cutting it crosswise into half-moon slices about 1/4 inch thick.

Step 6

Using tongs or a slotted spoon, move the chicken from the pot to a platter and let it cool. When you can handle it, pull the meat from the bones, discarding the bones and skin. Coarsely tear or chop the chicken and then return it to the pot along with the andouille.

Step 7

Cook the gumbo, stirring now and then, until the sausage has softened and everything has come together into a rich, flavorful, slightly thickened stew, about 30 minutes more.

Step 8

Remove the pot from the heat. (You can cool, cover, and refrigerate the gumbo for up to 2 days to allow the flavors to meld. Skim any fat from the surface of the gumbo and discard. Warm the gumbo over low heat prior to continuing.)

Step 9

Stir in the scallions and parsley. Serve the gumbo in bowls over rice or with rice on the side, garnished with more scallions.